Introduction to GIS ModelingIntroduction to GIS Modeling Week 4 — Measuring Distance and Connectivity Week 4 — Measuring Distance and Connectivity

GEOG 3110 –University of DenverGEOG 3110 –University of Denver

Simple vs. weighted distance; Proximity and Simple vs. weighted distance; Proximity and movement; Accumulation surfaces; Identifying optimal movement; Accumulation surfaces; Identifying optimal

path(s); Narrowness; Viewsheds and visual exposure path(s); Narrowness; Viewsheds and visual exposure surfaces surfaces

Presented byPresented by Joseph K. BerryJoseph K. BerryW. M. Keck Scholar, Department of Geography, University W. M. Keck Scholar, Department of Geography, University

of Denverof Denver

Classes of Spatial Analysis OperatorsClasses of Spatial Analysis Operators

(Berry)

……all spatial analysis involves changing values (numbers) on a map(s) all spatial analysis involves changing values (numbers) on a map(s) as a mathematical or statistical function of the values as a mathematical or statistical function of the values

on that map or another map(s)on that map or another map(s)

(See MapCalc Applications, “Cross-Reference” for a cross reference of MapCalc operations and those of other systems))(See MapCalc Applications, “Cross-Reference” for a cross reference of MapCalc operations and those of other systems))

An Analytic Framework for GIS ModelingAn Analytic Framework for GIS Modeling

(Berry)(Berry)

Proximity operationsProximity operations involve measuring involve measuring distance and connectivity among map locations distance and connectivity among map locations

(GIS Modeling Framework paper)(GIS Modeling Framework paper)

Distance and Connectivity FundamentalsDistance and Connectivity Fundamentals

(Berry)

S, SL, 2P

S route

S, SL, 2P

S, SL, 2P

Distance “Waves” Distance “Waves” (Simple and Effective Proximity)(Simple and Effective Proximity)

(Linked slide show DIST)(Linked slide show DIST)

(Berry)

Variable-Width Buffers Variable-Width Buffers (Simple vs. Uphill Proximity)(Simple vs. Uphill Proximity)

Simple BufferSimple Buffer– “as-the-crow-flies” proximity to – “as-the-crow-flies” proximity to the road; the road; no absolute or relative barriersno absolute or relative barriers are are considered; dark blue line indicates the full considered; dark blue line indicates the full simple buffer reach (polygon)simple buffer reach (polygon)

(Berry)

Clipped BufferClipped Buffer– – simple proximity for simple proximity for just the just the landland areas areas

Uphill BufferUphill Buffer– simple proximity to the road – simple proximity to the road for just the areas that are for just the areas that are uphill from the uphill from the roadroad; absolute barrier (uphill only– ; absolute barrier (uphill only– absolutely no downhill steps) absolutely no downhill steps)

DownhillDownhill

Distance and Connectivity OperationsDistance and Connectivity Operations

DRAIN -- Creates a map indicating the number of steepest DRAIN -- Creates a map indicating the number of steepest paths (optimal path density) from a set of locations along paths (optimal path density) from a set of locations along a surface.a surface.

RADIATE -- Creates a map indicating areas that are visible RADIATE -- Creates a map indicating areas that are visible from locations specified on the 'viewers map'. from locations specified on the 'viewers map'.

SPAN -- Creates a map indicating the narrowness within SPAN -- Creates a map indicating the narrowness within all non-zero areas on a map. all non-zero areas on a map.

SPREAD -- Creates a map indicating the shortest effective SPREAD -- Creates a map indicating the shortest effective distance from specified cells to all other locations. distance from specified cells to all other locations.

STREAM -- Creates a map identifying the steepest STREAM -- Creates a map identifying the steepest downhill route along a surface (optimal path). downhill route along a surface (optimal path).

(Berry)

Distance Techniques Distance Techniques (Exercise 4, Q1)(Exercise 4, Q1)

Calculating Simple/Weighted Proximity …Calculating Simple/Weighted Proximity …

SPREADSPREAD Roads TO 20 Simply FOR Roads_simpleprox Roads TO 20 Simply FOR Roads_simpleprox

SPREADSPREAD Roads TO 20 OVER Elevation Uphill Only Roads TO 20 OVER Elevation Uphill Only Simply FOR Roads_uphillproxSimply FOR Roads_uphillprox

RENUMBERRENUMBER Covertype ASSIGNING 0 TO 1 Covertype ASSIGNING 0 TO 1 ASSIGNING 3 TO 2 ASSIGNING 7 TO 3 ASSIGNING 3 TO 2 ASSIGNING 7 TO 3 FOR Hiking_friction FOR Hiking_friction

SPREADSPREAD Roads TO 60 THRU Hiking_friction Simply Roads TO 60 THRU Hiking_friction Simply FOR Road_hikingproxFOR Road_hikingprox

(Berry)

Measuring Distance as “Waves”Measuring Distance as “Waves” (Splash)(Splash)

(Berry)(See recommended reading on the CD “Calculating Effective Distance” for an in-depth discussion)(See recommended reading on the CD “Calculating Effective Distance” for an in-depth discussion)

Customizing MapCalc Displays Customizing MapCalc Displays (Shading Manager)(Shading Manager)

(Berry)

1) Set “User Defined Ranges”2) Set #Ranges = 143) Enter Range Breaks4) Set Color and Color Locks

1)1)2)2)

4)4)3)3)

Distance Techniques Distance Techniques (Exercise 4, Q2)(Exercise 4, Q2)

(Berry)

Boxes represent mapsLines represent processing steps

Locations

Roads Allroads

1= Any road0= All else

Covertype Hiking_friction

Bike_Hiking_friction

Ranch

1= Ranch0= All else

Ranch_prox

Step 1)Step 1) Establish off-road hiking Establish off-road hiking friction that considers the relative friction that considers the relative ease of traveling through various ease of traveling through various

cover types (done in Q1)cover types (done in Q1)

RENUMBERRENUMBER

Step 2)Step 2) Establish Establish on-road travel as on-road travel as 1= easiest with 0= 1= easiest with 0= all non-road areasall non-road areas

RENUMBERRENUMBER

Step 4)Step 4) Isolate the ranch location Isolate the ranch location

RENUMBERRENUMBER

Step 3)Step 3) Combine the on- and off- Combine the on- and off-road friction maps such that the on-road friction maps such that the on-road friction take precedent over the road friction take precedent over the

off-road frictionoff-road friction

COVERCOVER

Step 5Step 5) Calculate the effective ) Calculate the effective proximity from the ranch to proximity from the ranch to

everywhereeverywhere

SPREADSPREAD

Distance/Connectivity Techniques Distance/Connectivity Techniques (Exercise 4, Q2)(Exercise 4, Q2)

Friction MapFriction Map– identifies the relative – identifies the relative ease of travel through each map location ease of travel through each map location (grid cell)(grid cell)

Friction MapFriction Map

(See Beyond Mapping III online book , “Topic 14” for more information)(See Beyond Mapping III online book , “Topic 14” for more information)

(Berry)

Accumulation SurfaceAccumulation Surface

Accumulation SurfaceAccumulation Surface– identifies – identifies shortest distance (effective proximity steps)shortest distance (effective proximity steps)83.083.0

Establishing Optimal Paths Establishing Optimal Paths (Exercise 4, Q3)(Exercise 4, Q3)

(Berry)

StreamStream (Optimal Path) – (Optimal Path) – like a raindrop, the “like a raindrop, the “steepest steepest downhilldownhill” path identifies the ” path identifies the optimal pathoptimal path. If the surface is . If the surface is a proximity map, the optimal path identifies the shortest (not a proximity map, the optimal path identifies the shortest (not necessarily straight) route between any location on the necessarily straight) route between any location on the surface and the closest starting cell (point, line or polygon)surface and the closest starting cell (point, line or polygon)

Drain Drain (Optimal Path Density) – (Optimal Path Density) – accumulates the optimal paths accumulates the optimal paths from from many locationsmany locations. Higher “Drain” values indicate . Higher “Drain” values indicate locations that have numerous optimal paths passing locations that have numerous optimal paths passing through it (many through it (many uphill sourcesuphill sources moving through). moving through).

(Q3a)(Q3a)

(Q3b)(Q3b)

35.0

41.1 38.242.8

36.5 40.643.5

36.050.0

Repeat for next step Col 23, Row 19 and next, and next… until no more downhill stepsRepeat for next step Col 23, Row 19 and next, and next… until no more downhill steps

33.6

34.6

42.0 41.643.0

41.1 38.242.8

36.5 40.643.5

36.0 35.043.0

Col 22, Row 20Col 22, Row 20

(36.5 – 41.1) uphill (N)(36.5 – 38.2) uphill (NE)(36.5 – 40.6) uphill (E)(36.5 – 35.0) downhill (SE)(36.5 – 36.0) downhill (S)(36.5 – 43.0) uphill (SW)(36.5 – 43.5) uphill (W)(36.5 – 42.8) uphill (NW) …move to SE cellHow STREAM worksHow STREAM works

Discrete vs. Continuous BuffersDiscrete vs. Continuous Buffers

ContinuousBuffer

DiscreteBuffer

(Berry)

……ProximityProximity is formed by a series of continuous concentric rings– like is formed by a series of continuous concentric rings– like throwing a rock into a pond throwing a rock into a pond (each “step” is a one cell diagonal or orthogonal movement away)(each “step” is a one cell diagonal or orthogonal movement away)

Calculating Effective Proximity Calculating Effective Proximity (Travel-time)(Travel-time)

Superimposed Analysis GridSuperimposed Analysis Grid

100c x 100r = 10,000 cells

Effective ProximityEffective Proximity

…”proximity waves” ripple out along the

streets as if they were canals

…minutes away

TTime_animation.pptTTime_animation.ppt

(Berry)

Street Type as BarriersStreet Type as Barriers

Streets are calibrated…

…for ease of travel…

…“burn” the Roadsinto the analysis grid

(Vector to Raster)

Starting LocationStarting Location

…splash…

…”burn” the Starting location into the

analysis grid(Vector to Raster)

Transferring Travel-Time InformationTransferring Travel-Time Information

……the the Proximity WavesProximity Waves propagate propagate throughout the entire street pattern throughout the entire street pattern

assigning the travel-time values assigning the travel-time values to each location to each location

(farthest is 26 minutes in the upper-left corner)(farthest is 26 minutes in the upper-left corner)

……the proximity the proximity information is easily information is easily

transferred to a transferred to a desktop mapping desktop mapping

systemsystem……using using Pseudo-GridPseudo-Grid format format

(Raster to Vector)(Raster to Vector)

(Berry)

Utilizing Travel-Time InformationUtilizing Travel-Time Information

……a a Spatial JoinSpatial Join appends the appends the travel-time travel-time

information to information to the customer the customer

data tabledata table

……and is retrievable by clicking on and is retrievable by clicking on any customer location or through a any customer location or through a

geo-query requestgeo-query request

(families with 2 children that are more than 15 (families with 2 children that are more than 15 minutes—80 base cells—away)minutes—80 base cells—away)

(Berry)

Working with Travel-Time SurfacesWorking with Travel-Time Surfaces

……a travel-time map forms a travel-time map forms an an Accumulation SurfaceAccumulation Surface

whose values are whose values are continuously increasing continuously increasing

from the starting locationfrom the starting location(increasingly farther away)(increasingly farther away)

……the result is a the result is a bowl-like bowl-like surfacesurface with estimated time to with estimated time to

travel for every locationtravel for every location

……not a perfect bowl but warped and twisted not a perfect bowl but warped and twisted based on the based on the Relative and Absolute barriersRelative and Absolute barriers

to movementto movement

(Berry)

Optimal Path ConnectivityOptimal Path Connectivity

(Berry)

…the “steepest” downhill path along the Travel-Time surface identifies the quickest route

(optimal path)

Identifying Catchment Areas Identifying Catchment Areas (Optimal Path Density)(Optimal Path Density)

……the set of all optimal paths from all locations identify the set of all optimal paths from all locations identify Catchment AreasCatchment Areas characterized by travel-time to nearest ATM locationcharacterized by travel-time to nearest ATM location

(Berry)

Competition Analysis Competition Analysis (Relative Travel-time Position)(Relative Travel-time Position)

……subtracting the two surfaces derives subtracting the two surfaces derives relative travel-time advantagerelative travel-time advantage

……locations that are the same travel distance from locations that are the same travel distance from both stores result in zero– both stores result in zero–

PositivePositive values favor Colossal; values favor Colossal; NegativeNegative favor Kent favor Kent

(Berry)

Measuring NarrownessMeasuring Narrowness

The simple distance from a location to The simple distance from a location to all edge (boundary) locations is all edge (boundary) locations is computed. The minimum value of the computed. The minimum value of the sum of distances for opposing edge sum of distances for opposing edge cells is assigned… narrowness.cells is assigned… narrowness.

To improve performance, the To improve performance, the procedure is usually constrained to procedure is usually constrained to some maximum reach (e.g., all some maximum reach (e.g., all locations greater than 500 meters will locations greater than 500 meters will be set to 500)be set to 500)

SPAN Meadow WITHIN 9 FOR Cover_narrowSPAN Meadow WITHIN 9 FOR Cover_narrow

(See MapCalc Applications, “Characterizing Narrowness” for more information)(See MapCalc Applications, “Characterizing Narrowness” for more information) (Berry)

NarrownessNarrowness is defined as the “ is defined as the “shortest chordshortest chord connecting opposing edges.”connecting opposing edges.”

Establishing Visual ConnectivityEstablishing Visual Connectivity

RadiateRadiate – visual – visual exposure is calculated exposure is calculated bay a series of “waves” bay a series of “waves” that carry the tangent to that carry the tangent to beat.beat.

SimplySimply – viewshed – viewshedCompletelyCompletely – number of – number of “viewers” that see each location“viewers” that see each locationWeightedWeighted – viewer cell value is – viewer cell value is addedadded

(Berry)

Seen if new tangent exceeds Seen if new tangent exceeds all previous tangents along all previous tangents along the line of sight—the line of sight—

AtAt <Viewer_heightValue> <Viewer_heightValue> ThruThru <Screens_heightMap>) <Screens_heightMap>) OntoOnto <Target_heightMap> <Target_heightMap>

……like proximity, like proximity, Visual ConnectivityVisual Connectivity starts somewhere (starter cell) and starts somewhere (starter cell) and moves through geographic space by steps (wave front)– like a lighthouse moves through geographic space by steps (wave front)– like a lighthouse beam…beam…

Calculating Visual Exposure Calculating Visual Exposure (# Times Seen)(# Times Seen)

Visual exposure Visual exposure identifies identifies how many timeshow many times (count) each map (count) each map location is seen from a set of viewer locations location is seen from a set of viewer locations

(Berry)(Berry)

Visual Exposure from Extended FeaturesVisual Exposure from Extended Features

A visual exposure map identifies how many times each location is seen from an A visual exposure map identifies how many times each location is seen from an “extended eyeball” composed of numerous viewer locations (road network) “extended eyeball” composed of numerous viewer locations (road network)

(Berry)(Berry)

Weighted Visual Exposure Weighted Visual Exposure (Sum of Viewer Weights)(Sum of Viewer Weights)

Different road types are weighted by the relative number of cars per unit of time …the total Different road types are weighted by the relative number of cars per unit of time …the total “number of cars” replaces the “number of times seen” for each grid location“number of cars” replaces the “number of times seen” for each grid location

(See Beyond Mapping III, Topic 15, “Deriving and Using Visual Exposure Maps” for more information)(See Beyond Mapping III, Topic 15, “Deriving and Using Visual Exposure Maps” for more information) (Berry)(Berry)

Real-World Visual AnalysisReal-World Visual Analysis

Weighted visual Weighted visual exposure mapexposure map for an for an

ongoing visual ongoing visual assessment in a assessment in a

national recreation national recreation area— the project area— the project developed visual developed visual

vulnerability maps vulnerability maps from the reservoir in from the reservoir in the center of the park the center of the park and a major highway and a major highway running through the running through the

park. In addition, park. In addition, aesthetic mapsaesthetic maps were were generated based on generated based on visual exposure to visual exposure to

pretty and ugly pretty and ugly places in the parkplaces in the park

(Senior Honors Thesis by University of Denver Geography student Chris Martin, 2003)(Senior Honors Thesis by University of Denver Geography student Chris Martin, 2003)

(Berry)(Berry)

Variable-Width Buffers Variable-Width Buffers (Line-of-sight)(Line-of-sight)

Line-of-Sight BufferLine-of-Sight Buffer– identifies all – identifies all land locationsland locations (clipped) within 250m (clipped) within 250m that can be seen from the road… that can be seen from the road…

250m “viewshed” of the road250m “viewshed” of the road

(Berry)

Line-of-Sight Line-of-Sight ExposureExposure– notes – notes the the number of number of timestimes each location each location in the buffer is in the buffer is seenseen

Line-of-Sight NoiseLine-of-Sight Noise– locations hidden – locations hidden behind a ridge or farther away from a behind a ridge or farther away from a source (road) greatly decrease noise source (road) greatly decrease noise levels.levels.

Distance TechniquesDistance Techniques (Exercise 4, Q4)(Exercise 4, Q4)

Determining Determining visual connectivityvisual connectivity

from roads from roads and houses…and houses…

RadiateRadiate Roads Roads

over Elevation over Elevation to 100 completely to 100 completely for Ve_roadsfor Ve_roads  

SliceSlice Ve_roads Ve_roads into 5 into 5 for Ve_roads_slicedfor Ve_roads_sliced  

RadiateRadiate Housing over Elevation to 100 weighted for Ve_housing Housing over Elevation to 100 weighted for Ve_housing  

SliceSlice Ve_housing into 5 for Ve_housing_sliced Ve_housing into 5 for Ve_housing_sliced  

AnalyzeAnalyze average ve_roads_sliced with ve_housing_sliced for Vexposure average ve_roads_sliced with ve_housing_sliced for Vexposure   

(Berry)

On Your OwnOn Your Own (Exercise 4, Q5)(Exercise 4, Q5)

(Berry)

5-1) Using the Tutor25 database, determine the 5-1) Using the Tutor25 database, determine the average visual exposureaverage visual exposure (Vexposure (Vexposure map) map) for each of the administrative districtsfor each of the administrative districts (Districts map). (Districts map).

5-2) Using the Tutor25 database, identify the 5-2) Using the Tutor25 database, identify the visual exposurevisual exposure (Vexposure map from (Vexposure map from question #4) question #4) for a 300m simple buffer (3 cells) around roadsfor a 300m simple buffer (3 cells) around roads (Roads map). (Roads map).

5-3) Using the Tutor25 database, create a map (not just a display) that shows the 5-3) Using the Tutor25 database, create a map (not just a display) that shows the locations that have the highest (top 10%) visual exposure to houseslocations that have the highest (top 10%) visual exposure to houses (Housing map). (Housing map).

5-4) Using the Island database, create a map that identifies 5-4) Using the Island database, create a map that identifies locations that are fairly locations that are fairly steepsteep (15% or more on the Slope map) (15% or more on the Slope map) andand are westerly oriented are westerly oriented (SW, W and NW on (SW, W and NW on the Aspect map) the Aspect map) andand are within 1500 feet inland from the ocean are within 1500 feet inland from the ocean (hint: the analysis (hint: the analysis frame cell size is a “property” of any map display). frame cell size is a “property” of any map display).

5-5) Using the Agdata database, create a map that locates areas that have 5-5) Using the Agdata database, create a map that locates areas that have unusually unusually high phosphorous levelshigh phosphorous levels (one standard deviation above the mean on the 1997_Fall_P (one standard deviation above the mean on the 1997_Fall_P map) map) andand are within 300 feet of a “high yield pocket” are within 300 feet of a “high yield pocket” (top 10% on the (top 10% on the 1997_Yield_Volume map).1997_Yield_Volume map).

Screen grab the important maps and briefly describe your solution as a narrative flowchart. Screen grab the important maps and briefly describe your solution as a narrative flowchart. Must do threeMust do three (other 2 Optional extra credit)… (other 2 Optional extra credit)…

Optional QuestionsOptional Questions

(Berry)

Extended “Problems Extended “Problems with No Guidance” with No Guidance”

Weighted Visual Weighted Visual Exposure Density Exposure Density

SurfaceSurface

““Draining Forests”Draining Forests” for What?for What?

Pop Quiz PossibilityPop Quiz Possibility

……questions cover questions cover Class/LabClass/Lab material material and and Reading Reading assignments assignments to dateto date

— — you reviewed the previous class material and did the required reading for this class as well as, right?you reviewed the previous class material and did the required reading for this class as well as, right?

(Berry)